The effects of thermal energetics on three-dimensional hydrodynamic instabilities in massive protostellar disks. II. High-resolution and adiabatic evolutions

In this paper, the effects of thermal energetics on the evolution of gravit ationally unstable protostellar disks are investigated by means of three-di mensional hydrodynamic calculations. The initial states for the simulations correspond to stars with equilibrium, self-gravitating disks that are form ed early in the collapse of a uniformly rotating, singular isothermal spher e. In a previous paper (Pickett et al.), it was shown that the nonlinear de velopment of locally isentropic disturbances can be radically different tha n that of locally isothermal disturbances, even though growth in the linear regime may be similar. When multiple low-order modes grew rapidly in the s tar and inner disk region and saturated at moderate nonlinear levels in the isentropic evolution, the same modes in the isothermal evolution led to sh redding of the disk into dense arclets and ejection of material. In this pa per, we (1) examine the fate of the shredded disk with calculations at high er spatial resolution than the previous simulations had and (2) follow the evolution of the same initial state using an internal energy equation rathe r than the assumption of locally isentropic or locally isothermal condition s. Despite the complex structure of the nonlinear features that developed in t he violently unstable isothermal disk referred to above, our previous calcu lation produced no gravitationally independent, long-lived stellar or plane tary companions. The higher resolution calculations presented here confirm this result. When the disk of this model is cooled further, prompting even more violent instabilities, the end result is qualitatively the same-a shre dded disk. At least for the disks studied here, it is difficult to produce condensations of material that do not shear away into fragmented spirals. I t is argued that the ultimate fate of such fragments depends on how readily local internal energy is lost. On the other hand, if a dynamically unstable disk is to survive for very lo ng times without shredding, then some mechanism must mitigate and control a ny violent phenomena that do occur. The prior simulations demonstrated a ma rked difference in final outcome, depending upon the efficiency of disk coo ling under two different, idealized thermal conditions. We have here incorp orated an internal energy equation that allows for arbitrary heating and co oling. Simulations are presented for adiabatic models with and without arti ficial viscosity. The artificial viscosity accounts for dissipation and hea ting due to shocks in the code physics. The expected nonaxisymmetric instab ilities occur and grow as before in these energy equation evolutions. When artificial viscosity is not present, the model protostar displays behavior between the locally isentropic and locally isothermal cases of the last pap er; a strong two-armed spiral grows to nonlinear amplitudes and saturates a t a level higher than in the locally isentropic case. Since the amplitude o f the spiral disturbance is large, it is expected that continued transport of material and angular momentum will occur well after the end of the calcu lation at nearly four outer rotation periods. The spiral is not strong enou gh, however, to disrupt the disk as in the locally isothermal case. When ar tificial viscosity is present, the same disturbances reach moderate nonline ar amplitude, then heat the gas, which in turn greatly reduces their streng th and effects on the disk. Additional heating in the low-density regions o f the disk also leads to a gentle flow of material vertically off the compu tational grid. The energy equation and high-resolution isothermal calculati ons are used to discuss the importance and relevance of the different therm al regimes so far examined, with particular attention to applications to st ar and planet formation.